Question

Spinning Spinner 1st Simulation Colors Tally red 14 yellow 6 green 19 blue 1 2nd Simulation Colors Tally red 24 yellow 17 green 28 blue 11 3rd Simulation Colors Tally red 26 yellow 24 green 32 blue 38 Jill conducted three simulations of spinning a fair spinner (four sections of different colors--red, blue, yellow, green). The first simulation consisted of 40 spins, the second simulation consisted of 80 spins and the third simulation consisted of 120 spins. The results were recorded in the tables shown. Do the results for the green section follow the law of large numbers? Why or why not? A) no, because the probability of green is the same for each of the simulations. B) yes, because the probability of green is different for each of the simulations. C) no, because with each simulation, as the number of trials increase, the probabilities vary greatly and do not approach the theoretical probability of 1 4 . Eliminate D) yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of 1 4 .

Answer 1

The answer is D

Step-by-step explanation:

because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1

4

. The law of large numbers indicates that if an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions approaches p as the number of repetitions becomes arbitrarily large.

Answer 2

Answer: D

Step-by-step explanation: yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1/4.